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The Banach–Tarski Paradox

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  The Banach–Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 09:10 -0600
    Re: The Banach–Tarski Paradox Edgardo Alcantara <edgardoalcantara@carosseryrepair.org> - 2015-11-07 15:17 +0000
    Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 09:51 -0800
      Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 12:20 -0600
        Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 10:36 -0800
          Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 10:46 -0800
            Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 11:41 -0800
          Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 14:04 -0600
            Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 12:27 -0800
              Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 14:40 -0600
                Re: The Banach-Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-07 20:59 +0000
                Re: The Banach-Tarski Paradox noTthaTguY <abu.kuanysh05@gmail.com> - 2015-11-08 08:51 -0800
              Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 14:25 -0800
                Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 18:59 -0800
                  Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-09 07:59 -0800
            Re: The Banach-Tarski Paradox jimp@specsol.spam.sux.com - 2015-11-07 20:23 +0000
    Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-07 19:18 +0000
      Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 08:38 -0600
        Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-09 17:53 +0000
          Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 11:58 -0600
            Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-09 18:55 +0000
              Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 17:10 -0600
                Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 00:13 +0000
                  Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-09 17:12 -0800
                  Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 08:35 -0600
                    Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 15:08 +0000
                      Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 13:50 -0600
                        Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 23:47 +0000
                          Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 19:40 -0600
                            Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-11 02:32 +0000
                              Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 20:49 -0600

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#530893 — The Banach–Tarski Paradox

The Banach–Tarski Paradox
> https://www.youtube.com/watch?v=s86-Z-CbaHA

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#530895

W dniu Sat, 07 Nov 2015 09:10:57 -0600 użytkownik Sam Wormley napisał:

> The Banach–Tarski Paradox
>> https://www.youtube.com/watch?v=s86-Z-CbaHA
> 
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╚╩╚═╚╩╚═╚═╚╩╚═╝╚╝╚╝╚╝─

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#530933 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 7:11:19 AM UTC-8, Sam Wormley wrote:
> The Banach-Tarski Paradox


The Banach-Tarski "paradox", of the re-composition of 
non-measurable partitions of a ball to re-compose [1] to 
two copies of the ball, is examined vis-à-vis the 
result of Vitali, that, the unit line segment is 
recomposed via a similar form to another line segment 
of length "between one and three".

The re-Vitali-ization of measure theory, is then about 
that discretizing the points on the line doubles them.

[1] Via only rigid translations and rotation 
and no scaling nor shear

So, re-Vitali-ize measure theory (that there _is_ this 
iota-value in the real numbers, and discretizing or 
"counting" the points on the line doubles them).

Your video snippets are unacceptable in this text forum.

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#530941 — Re: The Banach-Tarski Paradox

On 11/7/15 11:51 AM, Ross A. Finlayson wrote:
> Your video snippets are unacceptable in this text forum.

   No true -- you can learn something, Ross, by watching the
   presentation.

   The Banach–Tarski Paradox
 > https://www.youtube.com/watch?v=s86-Z-CbaHA

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#530945 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 10:20:36 AM UTC-8, Sam Wormley wrote:
> On 11/7/15 11:51 AM, Ross A. Finlayson wrote:
> > Your video snippets are unacceptable in this text forum.
> 
>    No true -- you can learn something, Ross, by watching the
>    presentation.
> 
>    The Banach-Tarski Paradox
>  > https://www.youtube.com/watch?v=s86-Z-CbaHA
> 
> -- 

No, there is a video of the illusion 
of cutting and reconstructing a piece 
of paper with the missing part, that is 
an illusion because really all that is 
is imprecise, but beyond visual limits 
or as carrying the line.

No, the Banach-Tarski "paradox" or "B-T" 
has nothing to do with such illusions.

He does get up to combing the ball as 
of the topological examples that are 
often given (in regards to non-crossing 
spin about the ball), then without a 
transcript there's not much else to 
comment except that there's a difference 
between illusion and the topological 
argument of Banach-Tarski's ball-cutting 
and re-composition.

(Also I leave off the audio.)

Hah, he says "uncountable", then pushes a 
book of Yanofsky.

http://www.sci.brooklyn.cuny.edu/~noson/

(No comment.)

About Banach-Tarski and physics, you will 
find that there is no emplacement of trans-
finite cardinals anywhere in physics (except 
underneath measure theory, mute), then that 
an actual working emplacement of transfinite 
cardinals in physics will be about resolving 
the measurement / observer "paradoxes" as of 
"effect".

Anyone can learn anything from anything, but, 
there's not much to that.

So, what is (atomic) "spin"?

Here it arises from a spiral space-filling 
curve as a natural continuum.

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#530955 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 10:36:12 AM UTC-8, Ross A. Finlayson wrote:
> On Saturday, November 7, 2015 at 10:20:36 AM UTC-8, Sam Wormley wrote:
> > On 11/7/15 11:51 AM, Ross A. Finlayson wrote:
> > > Your video snippets are unacceptable in this text forum.
> > 
> >    No true -- you can learn something, Ross, by watching the
> >    presentation.
> > 
> >    The Banach-Tarski Paradox
> >  > https://www.youtube.com/watch?v=s86-Z-CbaHA
> > 
> > -- 
> 
> No, there is a video of the illusion 
> of cutting and reconstructing a piece 
> of paper with the missing part, that is 
> an illusion because really all that is 
> is imprecise, but beyond visual limits 
> or as carrying the line.
> 
> No, the Banach-Tarski "paradox" or "B-T" 
> has nothing to do with such illusions.
> 
> He does get up to combing the ball as 
> of the topological examples that are 
> often given (in regards to non-crossing 
> spin about the ball), then without a 
> transcript there's not much else to 
> comment except that there's a difference 
> between illusion and the topological 
> argument of Banach-Tarski's ball-cutting 
> and re-composition.
> 
> (Also I leave off the audio.)
> 
> Hah, he says "uncountable", then pushes a 
> book of Yanofsky.
> 
> http://www.sci.brooklyn.cuny.edu/~noson/
> 
> (No comment.)
> 
> About Banach-Tarski and physics, you will 
> find that there is no emplacement of trans-
> finite cardinals anywhere in physics (except 
> underneath measure theory, mute), then that 
> an actual working emplacement of transfinite 
> cardinals in physics will be about resolving 
> the measurement / observer "paradoxes" as of 
> "effect".
> 
> Anyone can learn anything from anything, but, 
> there's not much to that.
> 
> So, what is (atomic) "spin"?
> 
> Here it arises from a spiral space-filling 
> curve as a natural continuum.


What's a point?

Activating closed-captionining here, then 
some samples from the vid-feed:

"The Banach-Tarski paradox could actually 
happen in our real-world [....]"

No, no "paradoxes" happen at all, that's a 
contradicion in terms.

Heh, "Hadron Physics and Transfinite Set Theory", 
B.Augenstein 1984, _doesn't need transfinite cardinals_, 
just the B-T result.

"We are finite creatures...."

No, for example we know infinitely many numbers.

"Common sense applies to that which we can access."

No, sense applies to everything.

"... at the end of the day, history continues to show us 
that the Universe isn't strange."

What gumption to think that it was before (all day).

So:  re-Vitali-ize measure theory, for advancement 
of the mathematics underpinning topological results 
in measure theory as exemplified by the Banach-Tarski 
"theorem" that is about matching data.

Also: re-Vitali-ization _adds predictive power_ instead 
of losing it underneath the "foundations".

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#530980 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 10:46:37 AM UTC-8, Ross A. Finlayson wrote:
> On Saturday, November 7, 2015 at 10:36:12 AM UTC-8, Ross A. Finlayson wrote:
> > On Saturday, November 7, 2015 at 10:20:36 AM UTC-8, Sam Wormley wrote:
> > > On 11/7/15 11:51 AM, Ross A. Finlayson wrote:
> > > > Your video snippets are unacceptable in this text forum.
> > > 
> > >    No true -- you can learn something, Ross, by watching the
> > >    presentation.
> > > 
> > >    The Banach-Tarski Paradox
> > >  > https://www.youtube.com/watch?v=s86-Z-CbaHA
> > > 
> > > -- 
> > 
> > No, there is a video of the illusion 
> > of cutting and reconstructing a piece 
> > of paper with the missing part, that is 
> > an illusion because really all that is 
> > is imprecise, but beyond visual limits 
> > or as carrying the line.
> > 
> > No, the Banach-Tarski "paradox" or "B-T" 
> > has nothing to do with such illusions.
> > 
> > He does get up to combing the ball as 
> > of the topological examples that are 
> > often given (in regards to non-crossing 
> > spin about the ball), then without a 
> > transcript there's not much else to 
> > comment except that there's a difference 
> > between illusion and the topological 
> > argument of Banach-Tarski's ball-cutting 
> > and re-composition.
> > 
> > (Also I leave off the audio.)
> > 
> > Hah, he says "uncountable", then pushes a 
> > book of Yanofsky.
> > 
> > http://www.sci.brooklyn.cuny.edu/~noson/
> > 
> > (No comment.)
> > 
> > About Banach-Tarski and physics, you will 
> > find that there is no emplacement of trans-
> > finite cardinals anywhere in physics (except 
> > underneath measure theory, mute), then that 
> > an actual working emplacement of transfinite 
> > cardinals in physics will be about resolving 
> > the measurement / observer "paradoxes" as of 
> > "effect".
> > 
> > Anyone can learn anything from anything, but, 
> > there's not much to that.
> > 
> > So, what is (atomic) "spin"?
> > 
> > Here it arises from a spiral space-filling 
> > curve as a natural continuum.
> 
> 
> What's a point?
> 
> Activating closed-captioning here, then 
> some samples from the vid-feed:
> 
> "The Banach-Tarski paradox could actually 
> happen in our real-world [....]"
> 
> No, no "paradoxes" happen at all, that's a 
> contradiction in terms.
> 
> Heh, "Hadron Physics and Transfinite Set Theory", 
> B.Augenstein 1984, _doesn't need transfinite cardinals_, 
> just the B-T result.
> 
> "We are finite creatures...."
> 
> No, for example we know infinitely many numbers.
> 
> "Common sense applies to that which we can access."
> 
> No, sense applies to everything.
> 
> "... at the end of the day, history continues to show us 
> that the Universe isn't strange."
> 
> What gumption to think that it was before (all day).
> 
> So:  re-Vitali-ize measure theory, for advancement 
> of the mathematics underpinning topological results 
> in measure theory as exemplified by the Banach-Tarski 
> "theorem" that is about matching data.
> 
> Also: re-Vitali-ization _adds predictive power_ instead 
> of losing it underneath the "foundations".

HEP doesn't just "see" virtual particles, 
it "makes" them.

That's your blast radius right there.

So, theoretical physics is interested 
why that is so.

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#530984 — Re: The Banach-Tarski Paradox

On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
> No, the Banach-Tarski "paradox" or "B-T"
> has nothing to do with such illusions.

   What is the Banach-Tarski "paradox" about?



-- 

sci.physics is an unmoderated newsgroup dedicated
to the discussion of physics, news from the physics
community, and physics-related social issues.

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#530996 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 12:04:51 PM UTC-8, Sam Wormley wrote:
> On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
> > No, the Banach-Tarski "paradox" or "B-T"
> > has nothing to do with such illusions.
> 
>    What is the Banach-Tarski "paradox" about?
> 
> 

It is about making two from one, with 
otherwise a usual notion of conservation 
of area, for example, in the mathematics.

Then what there is, is that the "true foundations" 
numbers things, that "counting points" doubles 
what is found, vis-à-vis "meeting measurements".

That's mathematics and foundations in mathematics, 
then in physics it is about having via 4 or 5 
angles (the B-T result "chops" a ball into 4 or 5 
pieces), that then the pieces can be recomposed 
via rigid translation and rotation, into two "whole"
_copies_ of the ball.  The "paradox" is that that 
would violate the expectation of "conservation 
of space volume".

(It is about re-composition in a similar vein as 
physics has re-anti-de-normalization, or "normalization".)

This is a force effect, then about that being of 
the interface here of the point effect of the 
measurement effect (or observer effect) in the 
high energy physics or HEP.

Then the ring cyclotron should calorimeter itself 
at measurement, about a usual notion of conservation 
of conserved quantities being in effect, in physics.

This is about configuration of experiment and effect 
in measurement/observation, vis-à-vis effects in 
discretization in the mathematical and again in 
terms of "concrete fundamental mathematical resources".

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#531004 — Re: The Banach-Tarski Paradox

On 11/7/15 2:27 PM, Ross A. Finlayson wrote:
> It is about making two from one, with
> otherwise a usual notion of conservation
> of area, for example, in the mathematics.

   Not too shabby
 > https://en.wikipedia.org/wiki/Banach–Tarski_paradox

 > The Banach–Tarski paradox is a theorem in set-theoretic geometry,
 > which states the following: Given a solid ball in 3‑dimensional
 > space, there exists a decomposition of the ball into a finite number
 > of disjoint subsets, which can then be put back together in a
 > different way to yield two identical copies of the original ball.
 > Indeed, the reassembly process involves only moving the pieces around
 > and rotating them, without changing their shape. However, the pieces
 > themselves are not "solids" in the usual sense, but infinite
 > scatterings of points. The reconstruction can work with as few as
 > five pieces.[1]
 >
 > A stronger form of the theorem implies that given any two
 > "reasonable" solid objects (such as a small ball and a huge ball),
 > either one can be reassembled into the other. This is often stated
 > informally as "a pea can be chopped up and reassembled into the Sun"
 > and called the "pea and the Sun paradox".



-- 

sci.physics is an unmoderated newsgroup dedicated
to the discussion of physics, news from the physics
community, and physics-related social issues.

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#531011 — Re: The Banach-Tarski Paradox

On Sat, 07 Nov 2015 14:40:22 -0600, Sam Wormley wrote:

>> It is about making two from one, with
> 
>    Not too shabby
>

Sorry, Wormley.  It's not about that at all.

The BT-Paradox is all about the Axiom of Choice and nothing else.

In typical fashion, brain-dead Wormley picks isolated and dazzling
topics from the YouTube archives without understanding the big
picture.

Would you care to tell us about some more mathematical pathologies
that can be attributed to the Axiom of Choice?














>  > https://en.wikipedia.org/wiki/Banach–Tarski_paradox
> 
>  > The Banach–Tarski paradox is a theorem in set-theoretic geometry,
>  > which states the following: Given a solid ball in 3‑dimensional
>  > space, there exists a decomposition of the ball into a finite number
>  > of disjoint subsets, which can then be put back together in a
>  > different way to yield two identical copies of the original ball.
>  > Indeed, the reassembly process involves only moving the pieces around
>  > and rotating them, without changing their shape. However, the pieces
>  > themselves are not "solids" in the usual sense, but infinite
>  > scatterings of points. The reconstruction can work with as few as
>  > five pieces.[1]
>  >
>  > A stronger form of the theorem implies that given any two
>  > "reasonable" solid objects (such as a small ball and a huge ball),
>  > either one can be reassembled into the other. This is often stated
>  > informally as "a pea can be chopped up and reassembled into the Sun"
>  > and called the "pea and the Sun paradox".

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#531175 — Re: The Banach-Tarski Paradox

you may have seen the 5-piece decomposition
of a regular trigon to a regular tetragon

>  > scatterings of points. The reconstruction can work with as few as
>  > five pieces.[1]
>  >
>  > A stronger form of the theorem implies that given any two
>  > "reasonable" solid objects (such as a small ball and a huge ball),
>  > either one can be reassembled into the other. This is often stated
>  > informally as "a pea can be chopped up and reassembled into the Sun"
>  > and called the "pea and the Sun paradox".
> 
> 
> 
> -- 
> 
> sci.physics is an unmoderated newsgroup dedicated
> to the discussion of physics, news from the physics
> community, and physics-related social issues.

[toc] | [prev] | [next] | [standalone]

#531043 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 12:27:21 PM UTC-8, Ross A. Finlayson wrote:
> On Saturday, November 7, 2015 at 12:04:51 PM UTC-8, Sam Wormley wrote:
> > On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
> > > No, the Banach-Tarski "paradox" or "B-T"
> > > has nothing to do with such illusions.
> > 
> >    What is the Banach-Tarski "paradox" about?
> > 
> > 
> 
> It is about making two from one, with 
> otherwise a usual notion of conservation 
> of area, for example, in the mathematics.
> 
> Then what there is, is that the "true foundations" 
> numbers things, that "counting points" doubles 
> what is found, vis-à-vis "meeting measurements".
> 
> That's mathematics and foundations in mathematics, 
> then in physics it is about having via 4 or 5 
> angles (the B-T result "chops" a ball into 4 or 5 
> pieces), that then the pieces can be recomposed 
> via rigid translation and rotation, into two "whole"
> _copies_ of the ball.  The "paradox" is that that 
> would violate the expectation of "conservation 
> of space volume".
> 
> (It is about re-composition in a similar vein as 
> physics has re-anti-de-normalization, or "normalization".)
> 
> This is a force effect, then about that being of 
> the interface here of the point effect of the 
> measurement effect (or observer effect) in the 
> high energy physics or HEP.
> 
> Then the ring cyclotron should calorimeter itself 
> at measurement, about a usual notion of conservation 
> of conserved quantities being in effect, in physics.
> 
> This is about configuration of experiment and effect 
> in measurement/observation, vis-à-vis effects in 
> discretization in the mathematical and again in 
> terms of "concrete fundamental mathematical resources".

It would probably help the gallery here where 
there is relayed some of the models that use 
the "Banach-Tarski" "effect" in the explanation 
of where the configuration of experiment from 
four or five independent collectors / detectors 
is seeing twice the usual otherwise estimation 
of effect.

Again, this is about configuration of experiment 
and its very real effect on the interpretability 
and interpretation of results.

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#531107 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 2:25:29 PM UTC-8, Ross A. Finlayson wrote:
> On Saturday, November 7, 2015 at 12:27:21 PM UTC-8, Ross A. Finlayson wrote:
> > On Saturday, November 7, 2015 at 12:04:51 PM UTC-8, Sam Wormley wrote:
> > > On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
> > > > No, the Banach-Tarski "paradox" or "B-T"
> > > > has nothing to do with such illusions.
> > > 
> > >    What is the Banach-Tarski "paradox" about?
> > > 
> > > 
> > 
> > It is about making two from one, with 
> > otherwise a usual notion of conservation 
> > of area, for example, in the mathematics.
> > 
> > Then what there is, is that the "true foundations" 
> > numbers things, that "counting points" doubles 
> > what is found, vis-à-vis "meeting measurements".
> > 
> > That's mathematics and foundations in mathematics, 
> > then in physics it is about having via 4 or 5 
> > angles (the B-T result "chops" a ball into 4 or 5 
> > pieces), that then the pieces can be recomposed 
> > via rigid translation and rotation, into two "whole"
> > _copies_ of the ball.  The "paradox" is that that 
> > would violate the expectation of "conservation 
> > of space volume".
> > 
> > (It is about re-composition in a similar vein as 
> > physics has re-anti-de-normalization, or "normalization".)
> > 
> > This is a force effect, then about that being of 
> > the interface here of the point effect of the 
> > measurement effect (or observer effect) in the 
> > high energy physics or HEP.
> > 
> > Then the ring cyclotron should calorimeter itself 
> > at measurement, about a usual notion of conservation 
> > of conserved quantities being in effect, in physics.
> > 
> > This is about configuration of experiment and effect 
> > in measurement/observation, vis-à-vis effects in 
> > discretization in the mathematical and again in 
> > terms of "concrete fundamental mathematical resources".
> 
> It would probably help the gallery here where 
> there is relayed some of the models that use 
> the "Banach-Tarski" "effect" in the explanation 
> of where the configuration of experiment from 
> four or five independent collectors / detectors 
> is seeing twice the usual otherwise estimation 
> of effect.
> 
> Again, this is about configuration of experiment 
> and its very real effect on the interpretability 
> and interpretation of results.

I'd be interested if you could 
tell me where there is found 
any general "use" of the B-T 
theorem in physics then for 
where I will be looking under 
the hood to see if there is a
simpler numerical explanation 
via these discovered features of 
the numbers (and of counting 
and the numbers).

Basically I'm looking for 1-D 
or linear effects of discretization 
where the scaling factor is 2, and 
of 2-D or areal effects are 3,4,5 
(here where 4,5 are the least 
number of pieces via B-T that  
can be so re-composed).

Then the idea is to plug more 
mathematics into the mathematics 
of the mathematical physics already 
to so automatically equip the theory 
with expectations (for hypothesis 
testing via experiment as to not 
rejecting the null hypothesis).

Obviously most any scientist with 
rigor knows about hypothesis testing.
Here this is as to the relevance of 
quantum probabilities then as to 
that being of course within the 
"scientific method".

So, as I'm not a professional physicist, 
I'm hoping some experts will point to 
regular or apocryphally known experiments 
and their data that have seen Banach-Tarski 
introduced to the consideration.

I guess I have worked for the university 
before, but that was part of a computational 
biology project.  Yeah, that is also physics.

(This is where in the effective regime of the 
polar solvent called water there are usual 
molecular models of the simulation of 
biological processes, and about how they 
see effects of quantum level interactions 
as they work up to the kinematic.  This 
is for ab initio methods. ) 

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#531421 — Re: The Banach-Tarski Paradox

On Saturday, November 7, 2015 at 6:59:20 PM UTC-8, Ross A. Finlayson wrote:
> On Saturday, November 7, 2015 at 2:25:29 PM UTC-8, Ross A. Finlayson wrote:
> > On Saturday, November 7, 2015 at 12:27:21 PM UTC-8, Ross A. Finlayson wrote:
> > > On Saturday, November 7, 2015 at 12:04:51 PM UTC-8, Sam Wormley wrote:
> > > > On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
> > > > > No, the Banach-Tarski "paradox" or "B-T"
> > > > > has nothing to do with such illusions.
> > > > 
> > > >    What is the Banach-Tarski "paradox" about?
> > > > 
> > > > 
> > > 
> > > It is about making two from one, with 
> > > otherwise a usual notion of conservation 
> > > of area, for example, in the mathematics.
> > > 
> > > Then what there is, is that the "true foundations" 
> > > numbers things, that "counting points" doubles 
> > > what is found, vis-à-vis "meeting measurements".
> > > 
> > > That's mathematics and foundations in mathematics, 
> > > then in physics it is about having via 4 or 5 
> > > angles (the B-T result "chops" a ball into 4 or 5 
> > > pieces), that then the pieces can be recomposed 
> > > via rigid translation and rotation, into two "whole"
> > > _copies_ of the ball.  The "paradox" is that that 
> > > would violate the expectation of "conservation 
> > > of space volume".
> > > 
> > > (It is about re-composition in a similar vein as 
> > > physics has re-anti-de-normalization, or "normalization".)
> > > 
> > > This is a force effect, then about that being of 
> > > the interface here of the point effect of the 
> > > measurement effect (or observer effect) in the 
> > > high energy physics or HEP.
> > > 
> > > Then the ring cyclotron should calorimeter itself 
> > > at measurement, about a usual notion of conservation 
> > > of conserved quantities being in effect, in physics.
> > > 
> > > This is about configuration of experiment and effect 
> > > in measurement/observation, vis-à-vis effects in 
> > > discretization in the mathematical and again in 
> > > terms of "concrete fundamental mathematical resources".
> > 
> > It would probably help the gallery here where 
> > there is relayed some of the models that use 
> > the "Banach-Tarski" "effect" in the explanation 
> > of where the configuration of experiment from 
> > four or five independent collectors / detectors 
> > is seeing twice the usual otherwise estimation 
> > of effect.
> > 
> > Again, this is about configuration of experiment 
> > and its very real effect on the interpretability 
> > and interpretation of results.
> 
> I'd be interested if you could 
> tell me where there is found 
> any general "use" of the B-T 
> theorem in physics then for 
> where I will be looking under 
> the hood to see if there is a
> simpler numerical explanation 
> via these discovered features of 
> the numbers (and of counting 
> and the numbers).
> 
> Basically I'm looking for 1-D 
> or linear effects of discretization 
> where the scaling factor is 2, and 
> of 2-D or areal effects are 3,4,5 
> (here where 4,5 are the least 
> number of pieces via B-T that  
> can be so re-composed).
> 
> Then the idea is to plug more 
> mathematics into the mathematics 
> of the mathematical physics already 
> to so automatically equip the theory 
> with expectations (for hypothesis 
> testing via experiment as to not 
> rejecting the null hypothesis).
> 
> Obviously most any scientist with 
> rigor knows about hypothesis testing.
> Here this is as to the relevance of 
> quantum probabilities then as to 
> that being of course within the 
> "scientific method".
> 
> So, as I'm not a professional physicist, 
> I'm hoping some experts will point to 
> regular or apocryphally known experiments 
> and their data that have seen Banach-Tarski 
> introduced to the consideration.
> 
> I guess I have worked for the university 
> before, but that was part of a computational 
> biology project.  Yeah, that is also physics.
> 
> (This is where in the effective regime of the 
> polar solvent called water there are usual 
> molecular models of the simulation of 
> biological processes, and about how they 
> see effects of quantum level interactions 
> as they work up to the kinematic.  This 
> is for ab initio methods. )

Seems B-T is as often as not used as an 
example of "mathematics not applying to 
physics", but see for example this discussion 
about that "functional analysis uses only 
measurable sets".

http://physics.stackexchange.com/questions/20370/does-the-banach-tarski-paradox-contradict-our-understanding-of-nature

There are at least two things to consider 
with regards to B-T, mathematics, and physics.

One is that in terms of continuum analysis, 
that non-measurable sets don't have any 
particular analog to, say, Nyquist/Shannon 
or otherwise information/signal terms of 
the continuous/discrete.  So, there aren't 
any non-measurable "sets of points of real 
field elements" in usual field theories.

Still, when applied to "any continuum in 
mathematics", physics would be at a loss 
as to how basically Pauli exclusion fails, 
with this re-composability to two copies 
from one, that "point individuation" as 
discretization fills the point.  You may 
note that these 4 or 5 B-T parts _only 
exactly double_ the ball, i.e., B-T parts 
don't recompose back to the original ball.

So, it is then left to that "the usual 
mathematics of physics doesn't suitably 
exclude this case of variety, so, throw 
out continuum analysis altogether".  This 
leads to rather poor results where otherwise 
the usual notion of fields is as of 
continuous fields.

The ideal notion should be to look to how 
measurement / observation as we know is in 
effect then is really as of some counting / 
enumeration effect.  

So, the point here is to look for data that 
sees an exact doubling of the ball for a 
configuration of inputs that basically 
"triangulate", in the sense of establishing 
via various linear perspectives a confinement 
of the center of the ball, that in the three 
dimensions, the point is individuated via 
3,4,5, sides as it is so individuated via 
two sides "on" the line (where it has only 
one side "in" the line.

Notice this is a direct analog between
  measurement / observation 
and 
  counting / enumeration
in features in effect.

Also note this may be simple, tractable, and 
follows a neat retrofit of mathematical foundations 
with an augmented model of a continuum for 
foundations of mathematical physics.

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#531002 — Re: The Banach-Tarski Paradox

Sam Wormley <swormley1@gmail.com> wrote:
> On 11/7/15 12:36 PM, Ross A. Finlayson wrote:
>> No, the Banach-Tarski "paradox" or "B-T"
>> has nothing to do with such illusions.
> 
>   What is the Banach-Tarski "paradox" about?
 
You cut and paste a youtube video on the subject and you don't know?
 

-- 
Jim Pennino

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#530973

On Sat, 07 Nov 2015 09:10:57 -0600, Sam Wormley wrote:

> The Banach–Tarski Paradox
>

It's not a paradox, Wormley.  If you knew anything about foundational
mathematics -- which is certainly forever beyond your pathetic intellectual
reach -- you would realize that anything can be accomplished by modifying
the basic postulates of set theory.

Yes, just willy nilly change the postulates and one can do anything.

Just like you change the postulates of human nature so that you
can justify women in the science laboratory.

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#531402

On 11/7/2015 1:18 PM, Fabian Russell wrote:
> Just like you change the postulates of human nature

There's a fascinating phrase. I wonder what you mean by "postulates of 
human nature".

-- 
Odd Bodkin --- maker of fine toys, tools, tables

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#531447

On Mon, 09 Nov 2015 08:38:03 -0600, Odd Bodkin wrote:

> 
> There's a fascinating phrase. I wonder what you mean by "postulates of 
> human nature".
>

Human behavior, like set theory, can be seen to emerge from a number
of basic axioms or postulates.

Unlike set theory, however, these human "postulates" are not man-made*
but arise from the evolutionary development of the human organism.

The human "postulates" are the inborn instinctual drives and reactions
that define human behavior and all human possibility.  They are not
arbitrary.  They are set in stone.  Yet the progressive social leftist,
like Wormley, attempts to assign to the human being a different set
of such "postulates" to accommodate their wishes. 


*Note: The postulates of set theory are not actually man-made.  They
are self-evident entities and merely recognized or ascertained by man,

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#531448

On 11/9/2015 11:53 AM, Fabian Russell wrote:
> On Mon, 09 Nov 2015 08:38:03 -0600, Odd Bodkin wrote:
>
>>
>> There's a fascinating phrase. I wonder what you mean by "postulates of
>> human nature".
>>
>
> Human behavior, like set theory, can be seen to emerge from a number
> of basic axioms or postulates.
>
> Unlike set theory, however, these human "postulates" are not man-made*
> but arise from the evolutionary development of the human organism.
>
> The human "postulates" are the inborn instinctual drives and reactions
> that define human behavior and all human possibility.  They are not
> arbitrary.  They are set in stone.  Yet the progressive social leftist,
> like Wormley, attempts to assign to the human being a different set
> of such "postulates" to accommodate their wishes.

Fascinating. And what do you think those postulates are?

What, for example, are the postulates that have made you a computer 
hobbyist while others have no interest?

What are the postulates that fuel your general disdain for women when 
 >99% of the population do not share your view?

>
>
> *Note: The postulates of set theory are not actually man-made.  They
> are self-evident entities and merely recognized or ascertained by man,
>


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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